A system of non-linear partial differential equations modeling chemotaxis with sensitivy functions. (English) Zbl 1032.92006

Post, Katharina

Berlin: Humboldt-Univ., Mathematisch-Naturwissenschaftliche Fakultät II, electronic (1999).

Summary: We consider a system of nonlinear parabolic partial differential equations modeling chemotaxis, a biological phenomenon which plays a crucial role in aggregation processes in the life cycle of certain unicellular organisms. Our chemotaxis model introduces sensitivity functions which help describe the biological processes more accurately. In spite of the additional non-linearities introduced by the sensitivity functions into the equations, we obtain global existence of solutions for different classes of biologically realistic sensitivity functions and can prove convergence of the solutions to trivial and non-trivial steady states.

MSC:

92C17	Cell movement (chemotaxis, etc.)
35K55	Nonlinear parabolic equations
35Q92	PDEs in connection with biology, chemistry and other natural sciences